Worksheet: Rocket Propulsion

In this worksheet, we will practice using the rocket equation to calculate the motions of rockets and of the exhaust used to propel them.

Q1:

A large rocket has a mass of 2.00×10 kg at takeoff, and its engines
produce a thrust of 3.50×10 N.

Find the rocket’s initial vertically upward acceleration.

How much time is required for the rocket to attain a vertically upward velocity of 33.33 m/s, assuming constant mass and thrust?

Q2:

What exhaust speed is required to accelerate A rocket of mass 1,200 kg is in deep space.
The rocket accelerates from a speed of 0.80 km/s to a speed of 1.0 km/s
in a time of 5.0 s.
Using 50 kg of fuel, what must be the exhaust speed to produce this acceleration?

Q3:

A rocket accelerates vertically upward and
reaches a speed of 132 m/s.
Rocket fuel is burned, expelling
115 kg of exhaust from the rocket
vertically downward at 1,360 m/s.
The time taken for the rocket to
complete its acceleration was 12.4 s.
What was the mass of the rocket when fully loaded with fuel?
Ignore air resistance.

Q4:

An unfueled rocket has a mass of 1,370 kg.
The rocket must be loaded with sufficient fuel
to reach a vertically upward speed of 677 m/s
after 25.0 s of acceleration. The rocket ejects
exhaust from burned fuel vertically downward at
1,500 m/s.
What is the minimum mass of fuel that the rocket must be loaded with? Ignore air resistance.

Q5:

A spacecraft is moving uniformly in deep space where gravitational forces are negligible. At the instant 𝑡, the spacecraft’s engine is activated for a 30 s time interval, during which exhaust is ejected from the spacecraft at a rate of 2.0×10 kg/s with the exhaust moving at a speed of 2.5×10 m/s. The spacecraft’s mass before ejecting any exhaust is 2.0×10 kg.

What magnitude force is applied to the spacecraft by the engine while it is activated?

A5.0×10 N

B5.5×10 N

C2.2×10 N

D2.0×10 N

E4.0×10 N

What is the magnitude of the spacecraft’s acceleration at the instant 𝑡?

What is the magnitude of the spacecraft’s acceleration at the instant 𝑡=15s?

What is the magnitude of the spacecraft’s acceleration at the instant 𝑡=30s?